** The 240 Root Vectors of E8 Decompose into 40 Hexads Under the Weyl Group Subgroup S₃ — E8 Intelligence Research

** The Weyl group of E8 (order 696,729,600) contains a subgroup isomorphic to S₃ that preserves a 40-element orbit structure on the 240 roots. Each orbit forms a hexad whose inner products realize a specific signed configuration. This is *actual* E8 geometry — it's how the roots are organized under the maximal subgroup W(E7) × S₃. - ** Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com